and other level lines of f(x,y) = x^3 + y^3 - 3x*y

The level curves of the function

f(x,y) = x^3 + y^3 -3*x*y

can be computed from the ODE:

c'(t) = Rot90(grad f)(c(t))

where grad f vanishes at the origin [x,y] = [0,0],

where the Folium Of Descartes has a double point singularity and grad f vanishes at

[x,y] = [1,1], where f has a local minimum.

f(x,y) = x^3 + y^3 -3*x*y

can be computed from the ODE:

c'(t) = Rot90(grad f)(c(t))

where grad f vanishes at the origin [x,y] = [0,0],

where the Folium Of Descartes has a double point singularity and grad f vanishes at

[x,y] = [1,1], where f has a local minimum.

The level curves of the folium polynomial are individually computed as solutions of an ODE.

Therefore they can be treated as parametrized curves.